The last 6 years the snow pack has been less then average. Even then there were some snowfields high on the mountain with a well worn walking path into late June.
I was up on the trail in late May back in the last heavy snow year. There was snow all the way down to about 9500 feet that year in late May, which persisted into early July.
I think you should plan on some snow above trail camp up to trail crest. There will also be a large snowfield close to the summit which you will need to cross. There should be a well worn path, icy in the morning and evening but warm and slushy during the day.
Cetainly a warming sunny trend or continued snow could change how much snow will be left over by then.
I would plan on taking an Ice Axe/ Crampons until the final few winter months play out. You can follow the snowpack with this grid.
http://cdec.water.ca.gov/cgi-progs/current/PLOT_SWC